reserve x,x1,x2,y,y9,y1,y2,z,z1,z2 for object,P,X,X1,X2,Y,Y1,Y2,V,Z for set;

theorem Th23:
  for f being Function holds dom <:f,X,Y:> c= dom f & rng <:f,X,Y :> c= rng f
proof
  let f be Function;
  <:f,X,Y:> c= f by Th22;
  hence thesis by RELAT_1:11;
end;
